Letís think about a logical example:
When somebody ask you how many people (whom you know) love you, you will easily be confused. But if you were asked how many of them you love, it will be much easier for you to answer.

This example implies a physical aspect: we can not count how many objects in the universe which exert the gravitational force on the earth but we can aggregate all the gravitational forces which the earth exerts on every object in the universe. Why's that. Thatís because the earth is unique. It is like you are unique. Only you can feel your love with some people meanwhile you hardly can know how many of your friends really love you. This is also true in case of the gravity. The gravitational field of the earth make the gravitational forces on every object in the universe. This gravitational field can be called GravityE2U. Thatís why we can unify all of the gravitational forces the earth exerts on every object in the universe. Therefore, in theory, we can make something like this:

We will make the new forces. These forces are equal each force of GravityE2U in size and in same direction as each force of GravityE2U. But instead of exerting on every other object, all these new forces exert on the earth only. According to the Newtonís 3rd law: the gravitational forces the earth exerts on the other object is equal and opposite to the forces the other object exerts on the earth. So, that mean the new forces will balance all the gravitational forces which every object in the universe exerts on the earth. And hence, in theory, these new forces can hold the earth in an absolutely inertial state forever (unless the earth collapse with another object such as a planet or a star).
This leads to an argument: an absolutely inertial state not only of the earth but also of every object in the universe really does exist. An equivalent conclusion is : an absolute reference frame really does exist.

Anybody tell me these arguments are true or false ? Thanks for any opinion.

The argument is false. You are forgetting that the sum of all gravitational forces acting on the earth is not zero, and consequently do not "hold the earth in an absolutely inertial state forever." How do we know this? Simple - the Earth orbits the sun precisely because the gravitational force of the sun acting on the Earth is so much greater than the sum of all the gravitational forces from all other objects in the universe. And since the Earth is in orbit about the sun that means it is not in an inertial frame.

But even if it was, you still have no argument. Suppose that there was a space ship not in orbit about any star but rather drifting in deep space with engines off far and far enough from any stars or other planets such that there is effectively zero gravitational force acting on it. So it just drifts along, in an inertial frame, interacting with nothing. To the residents of this space ship its velocity is zero; they have no reason to think otherwise. Now along comes a second drifting space ship, also with engines off. The residents of that second ship call their velocity 0 as well, and yet the two ships are moving relative to each other. The residents of each ship consider that the other ship has a velocity. Who's right? They both are, because velocities are relative. They can't agree on absolute velocity, - all they can agree on is the rate at which the two ships are moving relative to each other.

The argument is false. You are forgetting that the sum of all gravitational forces acting on the earth is not zero, and consequently do not "hold the earth in an absolutely inertial state forever." How do we know this? Simple - the Earth orbits the sun precisely because the gravitational force of the sun acting on the Earth is so much greater than the sum of all the gravitational forces from all other objects in the universe. And since the Earth is in orbit about the sun that means it is not in an inertial frame.

But even if it was, you still have no argument. Suppose that there was a space ship not in orbit about any star but rather drifting in deep space with engines off far and far enough from any stars or other planets such that there is effectively zero gravitational force acting on it. So it just drifts along, in an inertial frame, interacting with nothing. To the residents of this space ship its velocity is zero; they have no reason to think otherwise. Now along comes a second drifting space ship, also with engines off. The residents of that second ship call their velocity 0 as well, and yet the two ships are moving relative to each other. The residents of each ship consider that the other ship has a velocity. Who's right? They both are, because velocities are relative. They can't agree on absolute velocity, - all they can agree on is the rate at which the two ships are moving relative to each other.

First, I don't mean the gravitational forces acting on the earth is zero. I just said the new forces I made can balance the gravitational forces acting on the earth. Because the new forces are equal to the gravitational forces the earth exerts on the every other object. Then I'm aware that the gravitational force the sun acting on the earth is much greater than all other objects, but remember the sun is also among the objects which the gravitational forces the earth acting on. So the new forces also included the force which is equal (in size) to the gravitational force the sun acting on the earth , but in the opposite direction.

Second, your second idea about 2 spaceships is another problem which is irrelevant to the point of my proof. I also have the explanation for the situation between 2 spaceships but I'd like to separate 2 problems: One is existence of an absolute reference frame and two is the relativistic movement between 2 objects in the universe. In this post, I just prove that there is existent an absolute inertial reference frame which can be considered as the most superior ruler for the motion of every object in the universe. I will try to share my point about the second problem in another post.

Dan, if you mean there's no connection between the arguments : "existence of absolute inertial state" and "existence of absolute reference frame", I can explain more. In the absolute inertial state, the status of earth's motion is unique and invariable. So it can be described as a linear equation. We don't have to concern what this linear equation is, just be sure it's linear and unique. So when the linear equation is unique, it means an absolute reference frame to measure the motion of the earth is really existent.

I'm still struggling to understand your argument, and what you mean by "new forces." So let me try to restate what it is I think you are trying to say, and tell me if I have this right:

There is a net force of gravity from all objects on the universe acting on the Earth. If we could apply a new force to the Earth that is exactly equal and opposite in direction to this net gravitational force, the Earth would no longer be in orbit but instead would travel in a straight line, not accelerating, and hence would be in an inertial frame. You say that this inertial frame would be unique, I assume because no other object would have the same position and velocity. Do I have this right? If so, how does that lead to your position that there is an "absolute" reference frame? If you applied an equivalent "new force" to Mars, it too would travel of in a straight line, but in a different direction and velocity than Earth, so its inertial reference frame would also be unique. So which reference frame is "absolute?"

I'm still struggling to understand your argument, and what you mean by "new forces." So let me try to restate what it is I think you are trying to say, and tell me if I have this right:

There is a net force of gravity from all objects on the universe acting on the Earth. If we could apply a new force to the Earth that is exactly equal and opposite in direction to this net gravitational force, the Earth would no longer be in orbit but instead would travel in a straight line, not accelerating, and hence would be in an inertial frame. You say that this inertial frame would be unique, I assume because no other object would have the same position and velocity. Do I have this right? If so, how does that lead to your position that there is an "absolute" reference frame? If you applied an equivalent "new force" to Mars, it too would travel of in a straight line, but in a different direction and velocity than Earth, so its inertial reference frame would also be unique. So which reference frame is "absolute?"

The answer for your question is pretty obvious. That is the earth and the mars are existent in the same 4th dimension - the Time. Supposing that the earth and the mars in the absolute inertial state, A and A' are the position of the earth and the mars at now. B and B' are the position of the earth and the mars after 5 seconds. We don't have to concern where A, A', B and B' are. We just be sure they are existent and unique. So the speed of the earth after 5 seconds equal AB/5, of the mars after 5 seconds is A'B'/5. And we also don't concern how much these speeds are, just remember they are existent and unique. The existence of these speeds is the proof of the existence of the same absolute reference frame for both the earth and the mars.

How are A, B, A' and B' measured? They are positions, but measured relative to what? A person on Earth could argue that length AB is zero, whereas a person on Mars might say that length A'B' is zero (since both are in inertial reference frames). This does not mean that there is an absolute reference frame for both - how do you reach that conclusion?

The existence of point A, A', B and B' is independent of the view point of observers. Even you are standing on the earth or standing on the mars, you have to admit the truth that at each time point the earth and the mars do exist at somewhere in the universe. And their positions at a time point are unique. So the argument I explain here also don't rely on the view point of any observer. We just focus on the truth that the positions are existent and unique. It leads to another argument that the velocities of the earth and the mars are existent and unique. That's it.